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Pentagon area

Source: 2012-2013 SDML High School 2a Problem 10/2012-2013 SDML Middle School 2a Problem 15

August 25, 2016

geometrySDML High School2012-13 SDML Round 2

Problem Statement

Pentagon

ABCDE

is inscribed in a circle such that

ACDE

is a square with area

12

. What is the largest possible area of pentagon

ABCDE

\text{(A) }9+3\sqrt{2}\qquad\text{(B) }13\qquad\text{(C) }12+\sqrt{2}\qquad\text{(D) }14\qquad\text{(E) }12+\sqrt{6}-\sqrt{3}